The Sinkhorn algorithm, based on Entropic Regularized Optimal Transport (OT), has garnered significant attention due to its computational efficiency enabled by GPU-friendly matrix-vector multiplications. However, vanilla OT primarily deals with computations between the source and target nodes in a bipartite graph, limiting its practical application in real-world transportation scenarios. In this paper, we introduce the concept of Optimal Flow Transport (OFT) as an extension, where we consider a more general graph setting and the marginal constraints in vanilla OT are replaced by flow balance constraints. To obtain solutions, we incorporate entropic regularization into the OFT and introduce virtual flows for individual nodes to tackle the issue of potentially numerous isolated nodes lacking flow passages. Our proposition, the OFT-Sinkhorn algorithm, utilizes GPU-friendly matrix iterations to maintain flow balance constraints and minimize the objective function, and theoretical results for global convergence is also proposed in this paper. Furthermore, we enhance OFT by introducing capacity constraints on nodes and edges, transforming the OFT problem into a minimum-cost flow problem. We then present the Capacity-Constrained EOFT-Sinkhorn algorithm and compare it with the traditional Minimum cost flow (MCF) algorithm, showing that our algorithm is quite efficient for calculation. In particular, our EOFT-Sinkhorn is evaluated on high-precision and integer-precision MCF problems with different scales from one hundred to five thousand size, exhibiting significant time efficiency and the ability to approximate optimal solutions.

The capability of generalization is a cornerstone for the success of modern learning systems. For non-Euclidean data, e.g., graphs, that particularly involves topological structures, one important aspect neglected by prior studies is how machine learning models generalize under topological shifts. This paper proposes AdvDIFFormer, a physics-inspired graph Transformer model designed to address this challenge. The model is derived from advective diffusion equations which describe a class of continuous message passing process with observed and latent topological structures. We show that AdvDIFFormer has provable capability for controlling generalization error with topological shifts, which in contrast cannot be guaranteed by graph diffusion models, i.e., the generalization of common graph neural networks in continuous space. Empirically, the model demonstrates superiority in various predictive tasks across information networks, molecular screening and protein interactions

Neuronal morphology is essential for studying brain functioning and understanding neurodegenerative disorders. As acquiring real-world morphology data is expensive, computational approaches for morphology generation have been studied. Traditional methods heavily rely on expert-set rules and parameter tuning, making it difficult to generalize across different types of morphologies. Recently, MorphVAE was introduced as the sole learning-based method, but its generated morphologies lack plausibility, i.e., they do not appear realistic enough and most of the generated samples are topologically invalid. To fill this gap, this paper proposes **MorphGrower**, which mimicks the neuron natural growth mechanism for generation. Specifically, MorphGrower generates morphologies layer by layer, with each subsequent layer conditioned on the previously generated structure. During each layer generation, MorphGrower utilizes a pair of sibling branches as the basic generation block and generates branch pairs synchronously. This approach ensures topological validity and allows for fine-grained generation, thereby enhancing the realism of the final generated morphologies. Results on four real-world datasets demonstrate that MorphGrower outperforms MorphVAE by a notable margin. Importantly, the electrophysiological response simulation demonstrates the plausibility of our generated samples from a neuroscience perspective. Our code is available at [https://github.com/Thinklab-SJTU/MorphGrower](https://github.com/Thinklab-SJTU/MorphGrower).

Combinatorial drug recommendation involves recommending a personalized combination of medication (drugs) to a patient over his/her longitudinal history, which essentially aims at solving a combinatorial optimization problem that pursues high accuracy under the safety constraint. Among existing learning-based approaches, the association between drug substructures (i.e., a sub-graph of the molecule that contributes to certain chemical effect) and the target disease is largely overlooked, though the function of drugs in fact exhibits strong relevance with particular substructures. To address this issue, we propose a molecular substructure-aware encoding method entitled MoleRec that entails a hierarchical architecture aimed at modeling inter-substructure interactions and individual substructures’ impact on patient’s health condition, in order to identify those substructures that really contribute to healing patients. Specifically, MoleRec learns to attentively pooling over substructure representations which will be element-wisely re-scaled by the model’s inferred relevancy with a patient’s health condition to obtain a prior-knowledge-informed drug representation. We further design a weight annealing strategy for drug-drug-interaction (DDI) objective to adaptively control the balance between accuracy and safety criteria throughout training. Experiments on the MIMIC-III dataset demonstrate that our approach achieves new state-of-the-art performance w.r.t. four accuracy and safety metrics. Our source code is publicly available at https://github.com/yangnianzu0515/MoleRec.

Molecule representation learning (MRL) has been extensively studied and current methods have shown promising power for various tasks, e.g., molecular property prediction and target identification. However, a common hypothesis of existing methods is that either the model development or experimental evaluation is mostly based on i.i.d. data across training and testing. Such a hypothesis can be violated in real-world applications where testing molecules could come from new environments, bringing about serious performance degradation or unexpected prediction. We propose a new representation learning framework entitled MoleOOD to enhance the robustness of MRL models against such distribution shifts, motivated by an observation that the (bio)chemical properties of molecules are usually invariantly associated with certain privileged molecular substructures across different environments (e.g., scaffolds, sizes, etc.). Specifically, We introduce an environment inference model to identify the latent factors that impact data generation from different distributions in a fully data-driven manner. We also propose a new learning objective to guide the molecule encoder to leverage environment-invariant substructures that more stably relate with the labels across environments. Extensive experiments on ten real-world datasets demonstrate that our model has a stronger generalization ability than existing methods under various out-of-distribution (OOD) settings, despite the absence of manual specifications of environments. Particularly, our method achieves up to 5.9\% and 3.9\% improvement over the strongest baselines on OGB and DrugOOD benchmarks in terms of ROC-AUC, respectively. Our source code is publicly available at \url{https://github.com/yangnianzu0515/MoleOOD}.